April Break Assignment


GO TO:Directions , Resources , Scoring

Due: 1st Class day after April Break

Objective: Students will create their own Study Guide which can be used to prepare for the AP Calculus Exam and which can be shared with classmates.

Directions:

1.) Create a neat and well organized study guide using the topics list from our syllabus as a guide.
2.) Include at least one piece of information for every topic on the list. Information can include:

• definitions
• rules
• procedures
• formulas
• examples

I am NOT telling you to do all of the above for each topic. These are just suggestions.

3.) Bring your guide to class the first day after April Break
4.) In class we will exchange study guides and peer review a classmate's work.
5.) Make revisions to your Study Guide.

Because of steps 4 and 5, it is ESSENTIAL that everybody complete this assignment on time and bring it to class. If you do not you will not only be impacting your work, but a classmate's ability to complete the assignment as well.

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Resources:

You can get a list of topics below. Use this as a starting point. Other resources that will be help full are:

• your notes
• handouts (especially packets, like the Parametrics Packet, Diff-E-Q Packet and Power Series Packet)
• textbook
• online resources

Click Here for BC Calculus Key Topics PDF


BC Calculus - Key Topics Covered:

Limits and Continuity

• Limits
  1. informal approach (including one-sided limits)
     1. numerical approach using a graphing calculator
     2. graphical approach using a graphing calculator
     3. algebraic techniques
  2. properties of limits
  3. limits and infinity, asymptotic and end behavior
• Continuity
  1. An intuitive understanding
  2. Definition
  3. Intermediate-Value Theorem

The Derivative

• Average Rate of Change
• The derivative of a function at a point
• The derivative function
• Techniques of differentiation
• The second derivative
• Derivatives of “special” functions
• Chain rule
• Linear approximation
• Implicit differentiation
• Related rate problems

Applying the Derivative

• L’Hospital’s rule
• Analysis of functions
  1. Critical points, relative and absolute extreme values, increasing/decreasing, first derivative test, inflection points, concavity, and second derivative test.
  2. Relating the graphs of f, f ′, and f ′′
• Mean Value Theorem and Rolle’s Theorem

The Definite Integral

• The integral as an accumulation
• Area under a curve
  1. Riemann sums
  2. Trapezoidal Approximation
• The Fundamental Theorem of Calculus (part 1)
• The Fundamental Theorem of Calculus (part 2)
• Antiderivatives and indefinite integrals
• Integration by substitution
• Integration by parts, partial fractions and improper integrals

Applications of the Definite Integral

• Area between two curves
• Average value
• Volume of solids

1. 1. with known cross-sectional area
2. 2. of revolution – disks/washers

• Analysis of functions given in polar form and parametric form.

Differential Equations

• Slope fields
• Separable differential equations
• Euler’s Method

Infinite Series

• Geometric series
• Testing for convergence and divergence
• Taylor series / polynomials
• Radius and intervals of convergence of power series
• Lagrange and alternating error bound

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Scoring:

Your study guide will be scored based on completeness, accuracy, organization and neatness. You should use the rubric below to guide you.

Click Here for the April Break Rubric PDF

April Break Assignment Rubric

SCORE	DESCRIPTION
4	üStudy Guide is complete, with all topics addressed in some way and with key information included. üStudy Guide is accurate. All information provided is correct and applies to the corresponding topic üStudy Guide is well organized. Topics are easy to recognize and the reader can recognize how information provided connects to the topic. Text features (bold, underline, fonts, etc.) are used to help the reader. üStudy Guide is neat. It is either typed and printed on unwrinkled paper or hand written meticulously.
3	üStudy Guide is mostly complete, with almost all topics addressed in some way and with most key information included. üStudy Guide is mostly accurate. Information provided is generally correct and applies to the corresponding topic üStudy Guide is mostly well organized. Topics are easy to recognize and the reader can recognize how information provided connects to the topic. üStudy Guide is neat. It is either typed and printed on unwrinkled paper or hand written meticulously.
2	üStudy Guide is partially complete, with all almost all topics addressed in some way but with some key information missing. üStudy Guide is partially accurate. Some information provided is incorrect or shows significant misunderstanding. üStudy Guide is partially organized. Topics are difficult to recognize or the reader may have difficulty recognizing how information provided connects to the topic. üStudy Guide is not neat. It is on wrinkled paper or is difficult to read.
1	üStudy Guide is incomplete. Major topics are missing. üStudy Guide is inaccurate. A significant amount of information provided is incorrect. üStudy Guide is not well organized. Topics difficult to recognize and the reader cannot recognize how information provided connects to the topic. üStudy Guide is not neat. It is on wrinkled paper or is difficult to read.

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